Journal article

THE NULL-CONE AND COHOMOLOGY OF VECTOR BUNDLES ON FLAG VARIETIES

Kari Vilonen, Ting Xue

REPRESENTATION THEORY | AMER MATHEMATICAL SOC | Published : 2016

Abstract

We study the null-cone of a semi-simple algebraic group acting on a number of copies of its Lie algebra via the diagonal adjoint action. We show that the null-cone has rational singularities in the case of SL3. We observe by example that the null-cone is not normal in general and that the normalization of the null-cone does not have rational singularities in general. This is achieved by computing cohomology of certain vector bundles on flag varieties.